Resampling Method for Generalized One-per-Stratum Sampling Designs

In areal surveys, one-per-stratum sampling is commonly used since it achieves spatial balance and improves estimation efficiency.The downside of such a design is that it is challenging to have a good variance estimator.In this paper, we propose a generalized one-per-stratum sampling design to generate a spatially balanced sample.The sample is used to get an M -estimator of the parameters in a spatial linear regression model, and the corresponding variance is estimated by a resampling method.Asymptotic properties of the M -estimator are investigated under the proposed one-per-stratum sampling design.Simulation studies show that the proposed one-per-stratum sampling design achieves good spatial balance, and the M -estimator is more efficient compared with existing designs.The resampling method is applied to investigate the relationship between soil erosion and slope in Iowa using a recent sample from the National Resources Inventory survey.